Problem: Simplify the following expression: $9\sqrt{63}$.
Explanation: First, try to factor a perfect square out of the radical. $= 9\sqrt{63}$ $= 9\sqrt{9 \cdot 7}$ Separate the radical and simplify. $= 9\sqrt{9} \cdot \sqrt{7}$ $= 9 \cdot 3 \cdot \sqrt{7}$ $= 27\sqrt{7}$